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Low-rank parity-check codes over finite commutative rings

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2024年 1-27页

作者： Kamche, Hermann Tchatchiem Kalachi, Herve Tale Djomou, Franck Rivel Kamwa Fouotsa, Emmanuel Univ Neuchatel Inst Math Neuchatel Switzerland Natl Adv Sch Engn Yaounde Dept Comp Engn Yaounde Cameroon Univ Dschang Fac Sci Dept Math & Comp Sci Dschang Cameroon Univ Bamenda Higher Teacher Training Coll Dept Math Bamenda Cameroon

Low-Rank Parity-Check (LRPC) codes are a class of rank metric codes that have many applications specifically in network coding and cryptography. Recently, LRPC codes have been extended to Galois rings which are a specific case of finite rings. In this paper, we first define LRPC codes over finite commutative local rings, which are bricks of finite rings, with an efficient decoder. We improve the theoretical bound of the failure probability of the decoder. Then, we extend the work to arbitrary finite commutative rings. Certain conditions are generally used to ensure the success of the decoder. Over finite fields, one of these conditions is to choose a prime number as the extension degree of the Galois field. We have shown that one can construct LRPC codes without this condition on the degree of Galois extension.

关键词： decoding algorithm Finite rings Galois extension LRPC codes Local rings Rank metric codes

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A New decoding Method for ReedSolomon Codes Based on FFT and Modular Approach

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IEEE TRANSACTIONS ON COMMUNICATIONS 2022年第12期70卷 7790-7801页

作者： Tang, Nianqi Han, Yunghsiang S. Huawei Technol Co Ltd Shenzhen 518129 Peoples R China Univ Elect Sci & Technol China Shenzhen Inst Adv Study Shenzhen 518110 Peoples R China

decoding algorithms for Reed-Solomon (RS) codes are of great interest for both practical and theoretical reasons. In this paper, an efficient algorithm, called the modular approach (MA), is devised for solving the Welch-Berlekamp (WB) key equation. By taking the MA as the key equation solver, we propose a new decoding algorithm for systematic RS codes. For (n, k) RS codes, where n is the code length and k is the code dimension, the proposed decoding algorithm has both the best asymptotic computational complexity O(n log (n - k) + (n - k) log(2) (n - k)) and the smallest constant factor achieved to date. By comparing the number of field operations required, we show that when decoding practical RS codes, the new algorithm is significantly superior to the existing methods in terms of computational complexity. When decoding the (4096, 3584) RS code defined over F-212, the new algorithm is 10 times faster than a conventional syndrome-based method. Furthermore, the new algorithm has a regular architecture and is thus suitable for hardware implementation.

关键词： decoding Codes Computational complexity Kernel Mathematical models Additives Fourier transforms Modular approach Reed-Solomon codes fast Fourier transform decoding algorithm

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Low-density parity-check-Feher quadrature phase shift keying signalling with frequency-offset compensated iterative demodulation and decoding algorithm

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IET COMMUNICATIONS 2014年第13期8卷 2264-2271页

作者： Yang, Zhihua Li, Yunhe Li, Huiyuan Qin, Jiao Zhang, Qinyu Cao, Bin Harbin Inst Technol Shenzhen Grad Sch Dept Elect & Informat Engn Shenzhen 518055 Peoples R China

The Feher quadrature phase shift keying (FQPSK) modulation is significantly susceptible to frequency and phase offsets under low signal-to-noise ratios. In this study, the authors proposed a serially concatenated signalling scheme with FQPSK modulation and low-density parity-check coding, which could efficiently resist residual frequency offset by employing an intended compensation algorithm. The designed maximum-likelihood estimation-enabled compensation algorithm is incorporated into the iterative concatenated demodulation-decoding process by using soft-input-soft-output-based maximum-a-posteriori-probability criterion. On the other side, the codeword sequence to be transmitted at the sender is re-arranged in a pre-configured order different from original codeword, in order to help the compensation algorithm diminish the impacts of frequency offsets. Simulation results show that the bit error rate of the proposed scheme can be improved efficiently up to three orders of magnitude with the frequency offsets from 100 to 700 ppm.

关键词： quadrature phase shift keying parity check codes maximum likelihood estimation iterative decoding demodulation probability error statistics frequency-offset iterative demodulation decoding algorithm Feher quadrature phase shift keying FQPSK modulation phase offsets signal-to-noise ratios low-density parity-check coding residual frequency offset maximum-likelihood estimation compensation algorithm iterative concatenated demodulation-decoding process soft-input-soft-output maximum-a-posteriori-probability criterion codeword sequence bit error rate

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Coding properties and automorphism groups of two classes of twisted generalized Reed-Solomon codes

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DESIGNS CODES AND CRYPTOGRAPHY 2025年 1-27页

作者： Jia, Xue Yue, Qin Sun, Huan Nanjing Univ Aeronaut & Astronaut Sch Math Nanjing 211100 Peoples R China Hubei Univ Hubei Key Lab Appl Math Wuhan 430071 Peoples R China Nanjing Univ Posts & Telecommun Coll Sci Nanjing 210023 Peoples R China

Twisted generalized Reed-Solomon (TGRS) codes as a generalization of generalized Reed-Solomon (GRS) codes have attracted a lot of attention from many researchers in recent years. In this paper, we investigate the conditions for the equality of two classes of TGRS codes with different parameters. Moreover, we construct the permutation automorphism groups of two classes of TGRS codes and show they are quasi-cyclic codes. Finally, building upon the Berlekamp-Massey algorithm for GRS codes, we show a decoding scheme for a class of MDS TGRS codes.

关键词： Twisted generalized Reed-Solomon codes Code equivalence Automorphism group decoding algorithm

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Magnetic Linear Encoder Based on Fuzzy Transition algorithm

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2025年 74卷

作者： Kang, Jian Dai, Yong Li, Huan Zhao, Jiarui Zhao, Yitao Hao, Shuanghui Harbin Inst Technol Sch Mechatron Engn Lab Intelligent Equipment Technol Harbin 150001 Peoples R China Shandong Taizhan Electromech Technol Co Ltd Zibo 255130 Peoples R China Shanxi Mech & Elect Design & Res Inst Co Ltd Taiyuan 030009 Peoples R China

In the research into linear displacement sensors, the main research targets are optical grating and magnetic grating-based displacement sensors. However, magnetic grating and optical grating techniques are horizontal measurement methods, which basically require a sliding substrate, a read head, and other components. The resulting magnetic grating or optical grating-based displacement sensors are large in size and cannot realize displacement measurements in small space or vertical measurement scenarios. In this article, a novel and highly accurate linear displacement sensor is designed for use in small space and vertical measurements that uses a completely different structure to conventional magnetic grating or optical grating-based displacement sensors. The proposed magnetic linear displacement sensor consists of two components: a moving shaft with nested magnets and a printed circuit board (PCB) that does not need a moving substrate or a sliding guide. The proposed sensor offers a simple structure, small size, high measurement stability, and high environmental adaptability. The sensor has a completely new structure, and no similar structural design has been reported in the current literature. A permanent magnet ring, an anti-oscillation interference structure, and a system circuit are designed in this article, and the possible oscillating interference, deterministic error, and random interference error characteristics of the sensor are analyzed. A linear displacement sensor decoding algorithm based on fuzzy transitions is designed based on the anti-oscillation structure: the corresponding anti-interference algorithm is added to it, and the effectiveness of the fuzzy transition decoding algorithm is then verified. Finally, an experimental platform is designed for nonlinear error calibration and swing error validation, and the performance specifications of the proposed displacement sensor are verified using this platform. The effect of oscillation error suppression i

关键词： Sensors Magnetic sensors Optical sensors Displacement measurement Gratings Optical variables measurement Oscillators Interference Adaptive optics Sensor phenomena and characterization decoding algorithm fuzzy transition linear encoder magnetic grating

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Fiber-Optic Current Sensing Based on Reflective Polarization-Bias-Added Structure

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IEEE SENSORS JOURNAL 2024年第1期24卷 292-302页

作者： Jiang, Run Zheng, Yuesheng Fuzhou Univ Coll Elect Engn & Automat Fuzhou 350108 Peoples R China Fujian Key Lab New Energy Generat & Power Convers Fuzhou 350108 Peoples R China

Polarimetric fiber-optic current-sensing technology is typically employed for measuring high current, as the low Verdet constant of optical fiber makes Faraday rotation not noticeable in low-current measurements and subsequently leads to low current sensitivity. To enhance current sensitivity, a polarimetric method based on a reflective polarization-bias-added (RPBA) structure is presented in this article. First, it is proved by the Jones matrix that current sensitivity would be compromised due to the constant term in the traditional sensing output. Then, the single-axis measurement method is employed to eliminate the constant term using the single-axis working (SAW) circulator. In consideration of the accuracy of subsequent signal decoding, the bias is generated by the RPBA structure to process optical signals between the circulator and the mirror. Next, a decoding algorithm based on parameter optimization is presented to restore the measured current from the photodetector output. Finally, the experimental results show that the current sensitivity of the presented method can be larger than 0.005 V/A under the premise of small measurement error in the vibration-and-temperature test. Compared with the existing polarimetric methods whose current sensitivity tends to be 0.002 V/A, the presented method has better current sensitivity without incurring additional sensor-head turns or optical devices.

关键词： Current sensitivity decoding algorithm measurement polarimetric fiber-optic current-sensing technology reflective polarization-bias-added (RPBA) structure

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LDPC decoding with locally informed dynamic scheduling based on the law of large numbers

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IET COMMUNICATIONS 2022年第6期16卷 634-648页

作者： Liang, Shuo Xie, Suipeng Liu, Xingcheng Wang, Zhongfeng Sun Yat Sen Univ Sch Elect & Informat Technol SEIT Guangzhou Peoples R China Guangzhou Xinhuo Univ Sch Informat Sci Guangzhou Peoples R China Southern Marine Sci & Engn Guangdong Lab Zhuhai Innovat Team Estuary Coast & Isl Reef Engn Zhuhai Peoples R China Nanjing Univ Sch Elect Sci & Engn Nanjing Peoples R China

The informed dynamic scheduling (IDS) strategies, in which the edge message with the maximum message-residual is updated preferentially, achieve remarkable error-correction performance when applied to low-density parity-check (LDPC) codes. However, the IDS strategies incur inferior convergence in iterative decoding owing to the greedy problem, which is called the update-relayed trend here. In order to solve the greediness, two locally informed dynamic scheduling algorithms based on the law of large numbers are proposed. The proposed decoding algorithms use random select of check nodes over a predefined update range (RSPUR) which effectively suppresses the propagation of the update-relayed trend and accordingly restrains the forming of multi-update cycles. Moreover, the decoding algorithm is further improved based on random select of check nodes over an adjustable update range (RSCAR). The update ranges are selected based on the law of large numbers. Therefore, the computational resources can be allocated more equitably by increasing iterations. Simulation results show that both the proposed algorithms achieve excellent performance in terms of throughput and convergence with low decoding complexity over the Additive White Gaussian Noise (AWGN) and the fading channels compared to the previous IDS strategies. Hence, the proposed algorithms behave excellently over the wireless channels.

关键词： maximum message residual error correction performance multiupdate cycles fading channels LDPC inferior convergence wireless channels check nodes AWGN channels low density parity check codes edge message telecommunication scheduling low decoding complexity IDS strategies informed dynamic scheduling strategies adjustable update range parity check codes predefined update range iterative decoding channel coding greedy problem locally informed dynamic scheduling algorithms iterative decoding owing decoding algorithm

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Investigating the Effect of Different Channel Coding on the Performance of Sparse Code Multiple Access over AWGN Channel

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WIRELESS PERSONAL COMMUNICATIONS 2023年 1-21页

作者： Muhammed, Younus A. Yousif, Raghad Z. Soran Univ Coll Sci Dept Comp Sci Soran KRG Iraq Salahaddin Univ Erbil Coll Sci Dept Phys Erbil KRG Iraq Catholic Univ Erbil Coll Informat Technol Dept IT Erbil KRG Iraq

The next generation of wireless communication systems requires simultaneous and reliable connectivity on a huge scale. Selecting the proper channel coding for sparse code multiple access (SCMA) as code domain non-orthogonal multiple access techniques is crucial for meeting the needs of the internet of things (IoT), which is the foundational technology in fifth generation wireless networks (5G). SCMA is a multiplexing technology that maximizes spectrum efficiency while increasing accessibility. In this research, the bit error rate (BER) of three joint systems has been compared: Joint Turbo code and SCMA (JTCSCMA), Joint low density parity check (LDPC) code and SCAM (JLC-SCMA), and Joint Polar code and SCMA (JPC-SCMA) for downlink sites supporting the IoT. Thus, the channel coder parameters of the proposed systems have been examined in an effort to enhance the overall performance of the combined systems. The simulation results demonstrated that the JPC-SCMA system outperformed other suggested systems over an AWGN channel while requiring less computational complexity. At BER 10(-4), the JPC-SCMA system exhibited an SNR improvement of 1 dB over JLC-SCMA and 2.8 dB over JTC. Additionally, at BER 10(-2), it was observed that JPC-SCMA produced a gain of 4.5 dB at iteration 5 with interleaved case.

关键词： SCMA Channel coding MPA decoding algorithm

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A subclass of q^m-ary Reed-Solomon codes and decoding of some rational GAG-codes

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SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES 2023年第2期17卷 850-870页

作者： Kabbouch, Oussama Najmeddine, Mustapha Univ Moulay Ismail Dept Math ENSAM Meknes Marjane 2 Meknes 50500 Morocco

In this paper, we introduce the notion of preserving distance codes (PD-codes) and we propose a decoding algorithm, using the error correcting pairs, for these codes in a particular case, without involving the duality. Then, we give a subclass of Reed Solomon codes which are primitive, and we give conditions for which these codes are PD-codes. Finally, we determine the minimum distance of some GAG-codes.

关键词： Error correcting pairs Reed Solomon codes GAG-codes decoding algorithm

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Convolutional Neural Decoder for Surface Codes

IEEE TRANSACTIONS ON QUANTUM ENGINEERING

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IEEE TRANSACTIONS ON QUANTUM ENGINEERING 2024年第1期5卷 1页

作者： Jung, Hyunwoo Ali, Inayat Ha, Jeongseok Korea Adv Inst Sci & Technol Sch Elect Engn Daejeon 34141 South Korea

To perform reliable information processing in quantum computers, quantum error correction (QEC) codes are essential for the detection and correction of errors in the qubits. Among QEC codes, topological QEC codes are designed to interact between the neighboring qubits, which is a promising property for easing the implementation requirements. In addition, the locality to the qubits provides unusual tolerance to local errors. Recently, various decoding algorithms based on machine learning have been proposed to improve the decoding performance and latency of QEC codes. In this work, we propose a new decoding algorithm for surface codes, i.e., a type of topological codes, by using convolutional neural networks (CNNs) tailored for the topological lattice structure of the surface codes. In particular, the proposed algorithm takes advantage of the syndrome pattern, which is represented as a part of a rectangular lattice given to the CNN as its input. The remaining part of the rectangular lattice is filled with a carefully selected incoherent value for better logical error rate performance. In addition, we introduce how to optimize the hyperparameters in the CNN, according to the lattice structure of a given surface code. This reduces the overall decoding complexity and makes the CNN-based decoder computationally more suitable for implementation. The numerical results show that the proposed decoding algorithm effectively improves the decoding performance in terms of logical error rate as compared to the existing algorithms on various quantum error models.

关键词： Codes Qubit decoding Lattices Machine learning algorithms Convolutional neural networks Surface treatment Convolutional neural network (CNN) decoding algorithm lattice structure surface codes topological quantum error correction codes

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